OK, I'll jump in. We co-sleep with our autistic 5 year old, who has sleep issues aplenty.
Lots of things may cause kicking. The easiest answer is to see if it's a bowel issue -- does he make a BM in the morning or at night? If he can do it before bedtime, his tummy will be calmer while sleeping and the kicking may be reduced. Make sure his bladder is COMPLETELY empty, too.
Another possibility is room temp. My DS kicks off his blanket, then gets cold at 3:30AM and thrashes around shivering. DH and I have learned to keep him lightly covered while half asleep -- even covering just part of of his body keeps him just warm enough to sleep peacefully.
The most difficult culprit to track down is dietary. Restless legs may be caused by a mineral deficiency, usually some combination of calcium, magnesium, potassium and zinc. Half a banana (rich in potassium) for breakfast consistently prevents nighttime leg cramps for me and DS. You may also try buying orange juice (naturally rich in magnesium) enriched with calcium and/or zinc, and offering that to DS for lunch. I've even heard of children who kick all night if they consume any sugar after 6 pm, and some autistic children who thrash in bed after eating gluten and/or casein for dinner...food dyes, esp. red dye #40, are another common cause for kicking and restlessness. We talk a lot about these sleep issues in the autism community, and every child seems to have a different food sensitivity. Be aware of what your DS is eating, esp. for dinner, and see if you can find a pattern in his nighttime behavior.
You can fix this problem, you just need to do a little detective work.